On a variational method for solving a class of $p$-Kirchhoff type problem

TL;DR

This paper introduces a variational approach to find multiple positive solutions for a class of $p$-Kirchhoff problems with sign-changing weights, expanding understanding of nonlinear differential equations.

Contribution

It develops a Nehari manifold method to establish the existence of multiple solutions for $p$-Kirchhoff problems with sign-changing weights, a novel application in this context.

Findings

Multiple positive solutions are proven to exist.

The Nehari manifold approach is effective for this class of problems.

Sign-changing weights are handled successfully in the analysis.

Abstract

In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.